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How are Cartesian coordinates used to locate a point on a plane?

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Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated. — analytic geometry The conic sections result from intersecting a plane with a double cone, as shown in the figure. There are three distinct families of conic sections: the ellipse (including the circle), the parabola (with one branch), and the hyperbola (with two branches).

In analytic geometry, the Cartesian coordinate system identifies the location of a point on a two-dimensional plane using two perpendicular axes that intersect at a reference point called the origin (0, 0).12

To locate a point, you use an ordered pair of numbers, denoted as (x, y):23

The x-coordinate: Represents the horizontal distance of the point from the origin. Positive values extend to the right, while negative values extend to the left.2
The y-coordinate: Represents the vertical distance of the point from the origin. Positive values extend upward, while negative values extend downward.2

These axes divide the plane into four quadrants based on the signs of the x and y values. By measuring the distance along each axis from the origin, you can precisely define the position of any point within the plane.23